Credits on sales don't affect Purchases Clearing (which is for managing purchases received vs invoiced).  Post the transaction in a test company if you want to confirm the GL entries before posting Live.  Generally a CM acts like a negative invoice.  Inventory up, reverse COGS, reverse revenue, negative AR... (plus all the extras like discounts, sales tax...).  If things don't go where you CPA wants them, use JE's to fix that.

The real question is whether you are crediting your customer, or their customer... and how to get them the refund.  The help files describe how to refund a customer.

Here is my dilemma although I still may be over-thinking this. This customer did not purchase the item from us. So am I not increasing my inventory of this item without a corresponding A/P transaction?

The negative AR is like AP, but because you do the CM on the customer side it's not technically AP (in Sage transaction data).  That's the tricky part... processing a payment from negative AR, which is where the help files can guide you.

Note: I am not an accountant... be sure to consult with a CPA on what they want to do from an accounting perspective.

Thanks for helping out. I am just going back and forth with this one. I am looking at it like if I was a retail store. A customer comes in to return a pair of jeans she bought at another store. We carry them, so we decide to allow the return. Would the cashier just put the jeans into inventory without any further transactions? I am just not sure how we can account for this "extra" piece of inventory.

I can only describe how to do things in Sage 100 terms, not give accounting advice.  Ask a CPA?

I just emailed her

Sage 100 does not care where the items from or if they purchased it from you originally.  It does not check either when creating a credit. If you credit a credit memo in Sales Order a credit will be created and the product put into inventory. Simple process.